Ta có: x=100

nên x+1=101

Ta có: \(f\left(x\right)=x^8-101x^7+101x^6-101x^5+...+101x^2-101x+25\)

\(=x^8-x^7\left(x+1\right)+x^6\left(x+1\right)-x^5\left(x+1\right)+...+x^2\left(x+1\right)-x\left(x+1\right)+25\)

\(=x^8-x^7-x^7+x^7+x^6-x^6-x^5+x^5-x^4+...+x^3+x^2-x^2-x+25\)

\(=-x+25\)

\(=-100+25=-75\)

Ta có: x=100

\(\Leftrightarrow x+1=101\)

Ta có: \(f\left(x\right)=x^{10}-101x^9+101x^8-101x^7+...+101x+2021\)

\(=x^{10}-x^9\cdot\left(x+1\right)+x^8\left(x+1\right)-x^7\left(x+1\right)+...+x\left(x+1\right)+2021\)

\(=x^{10}-x^{10}-x^9+x^9+x^8-x^8-x^7+...+x^2+x+2021\)

\(=x+2021\)

\(=100+2021=2121\)

f(100)=x⁸-(100+1)x⁷+(100+1)x⁶-(100+1)x⁵+....+(100+1)x²-(100+1)x+25

=x⁸-(x+1)x⁷+(x+1)x⁶-(x+1)x⁵+....+(x+1)x²-(x+1)x+25

=x⁸-x⁸-x⁷+x⁷+x⁶-x⁶-x⁵+...+x³+x²-x²-x+25

=25

vậy f(100)=25

Mk ko hiểu lắm! Hoàng Phúc

-x+25=25?

ai ket bn ko

giải hộ

f(100)=> x=100

=>x+1=101

thay x+1=101 ta được:

f(100)=x⁸-(x+1)x⁷+(x+1)x⁶-(x+1)x⁵+...+(x+1)x²-(x+1)x+25

=x⁸-(x⁸+x⁷)+(x⁷+x⁶)-(x⁶+x⁵)+...+(x³+x²)-(x²+x)+25

=x⁸-x⁸-x⁷+x⁷+x⁶-x⁶-x⁵+...+x³+x²-x²-x+25

=-x+25

=-100+25

=-75

-75 nha

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